Sequences Review

Front

What is a geometric sequence?

Back

A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

How do you find the common ratio in a geometric sequence?

Back

Divide any term by the previous term. For example, in the sequence -2, -10, -50, -250, the common ratio is -5.

Front

What is the formula for the nth term of a geometric sequence?

Back

t(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Front

What is an arithmetic sequence?

Back

A sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

Front

How do you find the common difference in an arithmetic sequence?

Back

Subtract any term from the previous term. For example, in the sequence 2, 8, 14, the common difference is 6.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

a(n) = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Front

What does the function f(x) = mx + b represent?

Back

It represents a linear function, where 'm' is the slope and 'b' is the y-intercept.

Front

How do you evaluate a function at a specific point?

Back

Substitute the value of x into the function. For example, f(12) = 2(12) + 17 = 41.

Front

What is the difference between arithmetic and geometric sequences?

Back

Arithmetic sequences have a common difference, while geometric sequences have a common ratio.

Front

What is a common ratio?

Back

The factor by which each term of a geometric sequence is multiplied to get the next term.